It isn't in your best interest to do that while you are married to her she will only make a big deal out of the fact that you want to have an extra martial affair and she may take you for everything have you because she is angry. This is a very touchy situation seeing that you have a child together you don't want to jeopardize her still allowing you to have full custody of your child. You should tell her that you want her to go or if you are that unhappy maybe you should start looking for another place to stay with your child this way you will have your separation and will be able to do as you please. I don't think that you should talk to your wife about having an affair it may have repercussions. You both need to separate maybe give her time to look for another place or you move out. You may not have courage to talk about this because your conscience is telling you not to do this while you are married.
Ask for a separation and tell her you are serious about it and do not want to stay with someone that doesn't show him any kind of affection. You have to be stern about it and let her know that you are totally serious about it maybe the way you told her before didn't sound like you were sure what you wanted. Tell her you no longer want to live with her in the same house you have been sharing and see what her response is to that.
Then what you are going to have to do is find the courage to tell her honestly that you are not happy and there for you are gong to find someone who can make you happy but make sure you are willing to take the risk of losing everything, especially if you decide to go outside your marriage and have an affair. What I suggest to you is to tell her when your child is not around because she may cause another fight and it is not healthy for your daughter to hear that. Tell her you haven't been happy for a long time now and you're tired of going without intimacy and the touch of a woman. Without you talking your wife into marriage counseling you might as well say your marriage is over you both need help dealing with your feelings and your anger towards each other.